Is there something similar to the iOS Developer Enterprise Program for Windows Phone 8 apps?
Yes, you can join the enterprise program by signing up for a Company account in the Windows Phone Dev Center. The process is called Company App Distribution.
In a nutshell, once your company account has been verified, you'll receive an ID that you'll provide to Symantec, who will generate an Enterprise Mobile Code Signing Certificate. You'll use this certificate to generate a token (that devices use to identify themselves with your enterprise) and to sign applications. The token and the apps can be distributed via e-mail, browser, MDM, or Company Hub.
E-mail and browser distribution are straight-forward, MDM occurs through a device management system such as Windows InTune. Company Hub is an on-device application that your organization develops for in-house application discovery, installation, and launch.
See the Windows Phone 8: Enterprise Development talk from the //Build/ conference for more information.